Perhaps the simplest and best-known form of tessellation is the jig-saw puzzle, in which a very simple shape, such as a rectangle or a circle, is covered with a multitude of pieces of irregular and usually distinct shape. A major characteristic of a jig-saw puzzle is the fact that it can only be assembled in one particular way. More sophisticated forms of tessellation have included the use of identical pieces which may be arranged to form a variety of shapes, such as so-called "polyominoes". A recent form of tessellation is disclosed in U.S. Pat. No. 4,133,152 to Penrose.
An example of polyominoes is the set of 29 different "pentacubes" which--when supplemented by a single extra pentacube which is a duplicate of one of the set of 29--forms bricks of four different shapes, each of volume equal to 150 unit cubes. This is disclosed in U.S. Pat. No. 3,065,970 to Besley, Nov. 27, 1962.
Three-dimensional puzzles have also been devised making use of sets of pieces derived from simple solid shapes, such as Piet Hein's Soma cube sold by Parker Brothers.